Question

Simplify: $ \dfrac{3}{4} \times \dfrac{5}{2} $

Answer 1

Hint: The given expression deals with operations on fractions. Fraction represents equal parts of a whole or a collection. Basic operations like addition, subtraction, multiplication and division can be done on fractions with ease. The given problem deals with multiplication of two fractions and finding the product.

Complete step-by-step answer:
In the given problem, we are required to multiply two fractions. Multiplication of fractions is an extremely easy task. In other words, we need to find the product of two fractions. To multiply two fractions, we just need to multiply their numerators and denominators separately and we can get the product of the two fractions.
So, $ \dfrac{3}{4} \times \dfrac{5}{2} $
 $ = $ $ \dfrac{{3 \times 5}}{{4 \times 2}} $
  $ = $ $ \dfrac{{15}}{8} $
Thus, $ \left( {\dfrac{3}{4} \times \dfrac{5}{2}} \right) $ = $ \left( {\dfrac{{15}}{8}} \right) $ .
Hence, the product of $ \left( {\dfrac{3}{4}} \right) $ and $ \left( {\dfrac{5}{2}} \right) $ is
$ \left( {\dfrac{{15}}{8}} \right) $ which is already in its lowest term.
So, the correct answer is “$ \left( {\dfrac{{15}}{8}} \right) $”.

Note: Addition and subtraction of two fractions is done after taking LCM of the denominators of the two fractions by multiplying both numerator and denominator of each fraction by same number and then simply adding or subtracting numerators of the fractions. Division of a fraction by another fraction is equivalent to multiplication of the first fraction by the multiplicative inverse of the second fraction.
After multiplication of fractions, we generally reduce the resultant product into its lowest form by cancelling the common divisors between numerator and denominator. But in the given problem, the resultant product $ \dfrac{{15}}{8} $ is already in its lowest form. Hence, there is no need to reduce it in its lowest term.